Gamma processes for time-dependent reliability of structures

In structural engineering, a distinction can be made between a structure’s resistance and its stress. A failure may then be defined as the event in which—due to deterioration—the resistance drops below the stress. This paper proposes a method to combine the two stochastic processes of deteriorating resistance and fluctuating load for computing the time-dependent reliability of a structural system. As deterioration is often uncertain and non-negative, it can best be regarded as a gamma process. A gamma process is a stochastic process with independent non-negative increments having a gamma distribution with identical scale parameter. The stress is assumed to be a stochastic process of random loads exceeding a certain threshold and occurring according to a Poisson process. The variability of the random loads is modelled by a peaks-over-threshold distribution (such as the generalised Pareto distribution). These stochastic processes of deterioration and load can be combined in a straightforward manner to perform a time-dependent reliability analysis.